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<center><h1>DirectedEulerianCycle.java</h1></center><p><br>

Below is the syntax highlighted version of <a href = "DirectedEulerianCycle.java">DirectedEulerianCycle.java</a>.
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<pre><tt><span class="comment">/******************************************************************************</span>
<span class="comment"> *  Compilation:  javac DirectedEulerianCycle.java</span>
<span class="comment"> *  Execution:    java DirectedEulerianCycle V E</span>
<span class="comment"> *  Dependencies: Digraph.java Stack.java StdOut.java</span>
<span class="comment"> *</span>
<span class="comment"> *  Find an Eulerian cycle in a digraph, if one exists.</span>
<span class="comment"> *</span>
<span class="comment"> ******************************************************************************/</span>

<span class="preproc">package</span><span class="normal"> edu</span><span class="symbol">.</span><span class="normal">princeton</span><span class="symbol">.</span><span class="normal">cs</span><span class="symbol">.</span><span class="normal">algs4</span><span class="symbol">;</span>

<span class="preproc">import</span><span class="normal"> java</span><span class="symbol">.</span><span class="normal">util</span><span class="symbol">.</span><span class="normal">Iterator</span><span class="symbol">;</span>

<span class="comment">/**</span>
<span class="comment"> *  The </span><span class="keyword">&lt;tt&gt;</span><span class="comment">DirectedEulerianCycle</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> class represents a data type</span>
<span class="comment"> *  for finding an Eulerian cycle or path in a digraph.</span>
<span class="comment"> *  An </span><span class="keyword">&lt;em&gt;</span><span class="comment">Eulerian cycle</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> is a cycle (not necessarily simple) that</span>
<span class="comment"> *  uses every edge in the digraph exactly once.</span>
<span class="comment"> *  </span><span class="keyword">&lt;p&gt;</span>
<span class="comment"> *  This implementation uses a nonrecursive depth-first search.</span>
<span class="comment"> *  The constructor runs in O(</span><span class="keyword">&lt;Em&gt;</span><span class="comment">E</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> + </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment">) time,</span>
<span class="comment"> *  and uses O(</span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment">) extra space, where </span><span class="keyword">&lt;em&gt;</span><span class="comment">E</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> is the</span>
<span class="comment"> *  number of edges and </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> the number of vertices</span>
<span class="comment"> *  All other methods take O(1) time.</span>
<span class="comment"> *  </span><span class="keyword">&lt;p&gt;</span>
<span class="comment"> *  To compute Eulerian paths in digraphs, see {</span><span class="type">@link</span><span class="comment"> DirectedEulerianPath}.</span>
<span class="comment"> *  To compute Eulerian cycles and paths in undirected graphs, see</span>
<span class="comment"> *  {</span><span class="type">@link</span><span class="comment"> EulerianCycle} and {</span><span class="type">@link</span><span class="comment"> EulerianPath}.</span>
<span class="comment"> *  </span><span class="keyword">&lt;p&gt;</span>
<span class="comment"> *  For additional documentation,</span>
<span class="comment"> *  see </span><span class="keyword">&lt;a</span><span class="normal"> </span><span class="type">href</span><span class="symbol">=</span><span class="string">"http://algs4.cs.princeton.edu/42digraph"</span><span class="keyword">&gt;</span><span class="comment">Section 4.2</span><span class="keyword">&lt;/a&gt;</span><span class="comment"> of</span>
<span class="comment"> *  </span><span class="keyword">&lt;i&gt;</span><span class="comment">Algorithms, 4th Edition</span><span class="keyword">&lt;/i&gt;</span><span class="comment"> by Robert Sedgewick and Kevin Wayne.</span>
<span class="comment"> * </span>
<span class="comment"> *  </span><span class="type">@author</span><span class="comment"> Robert Sedgewick</span>
<span class="comment"> *  </span><span class="type">@author</span><span class="comment"> Kevin Wayne</span>
<span class="comment"> *  </span><span class="type">@author</span><span class="comment"> Nate Liu</span>
<span class="comment"> */</span>
<span class="keyword">public</span><span class="normal"> </span><span class="keyword">class</span><span class="normal"> </span><span class="classname">DirectedEulerianCycle</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">    </span><span class="keyword">private</span><span class="normal"> </span><span class="usertype">Stack&lt;Integer&gt;</span><span class="normal"> cycle </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">null</span><span class="symbol">;</span><span class="normal">  </span><span class="comment">// Eulerian cycle; null if no such cylce</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Computes an Eulerian cycle in the specified digraph, if one exists.</span>
<span class="comment">     * </span>
<span class="comment">     * </span><span class="type">@param</span><span class="comment"> G the digraph</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="function">DirectedEulerianCycle</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>

<span class="normal">        </span><span class="comment">// must have at least one edge</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">E</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">==</span><span class="normal"> </span><span class="number">0</span><span class="symbol">)</span><span class="normal"> </span><span class="keyword">return</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// necessary condition: indegree(v) = outdegree(v) for each vertex v</span>
<span class="normal">        </span><span class="comment">// (without this check, DFS might return a path instead of a cycle)</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">outdegree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">)</span><span class="normal"> </span><span class="symbol">!=</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">indegree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                </span><span class="keyword">return</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// create local view of adjacency lists, to iterate one vertex at a time</span>
<span class="normal">        Iterator</span><span class="symbol">&lt;</span><span class="normal">Integer</span><span class="symbol">&gt;[]</span><span class="normal"> adj </span><span class="symbol">=</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">Iterator</span><span class="symbol">&lt;</span><span class="normal">Integer</span><span class="symbol">&gt;[])</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> Iterator</span><span class="symbol">[</span><span class="normal">G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">()];</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            adj</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">]</span><span class="normal"> </span><span class="symbol">=</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">adj</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">).</span><span class="function">iterator</span><span class="symbol">();</span>

<span class="normal">        </span><span class="comment">// initialize stack with any non-isolated vertex</span>
<span class="normal">        </span><span class="type">int</span><span class="normal"> s </span><span class="symbol">=</span><span class="normal"> </span><span class="function">nonIsolatedVertex</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>
<span class="normal">        </span><span class="usertype">Stack&lt;Integer&gt;</span><span class="normal"> stack </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> Stack</span><span class="symbol">&lt;</span><span class="normal">Integer</span><span class="symbol">&gt;();</span>
<span class="normal">        stack</span><span class="symbol">.</span><span class="function">push</span><span class="symbol">(</span><span class="normal">s</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// greedily add to putative cycle, depth-first search style</span>
<span class="normal">        cycle </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> Stack</span><span class="symbol">&lt;</span><span class="normal">Integer</span><span class="symbol">&gt;();</span>
<span class="normal">        </span><span class="keyword">while</span><span class="normal"> </span><span class="symbol">(!</span><span class="normal">stack</span><span class="symbol">.</span><span class="function">isEmpty</span><span class="symbol">())</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">            </span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> stack</span><span class="symbol">.</span><span class="function">pop</span><span class="symbol">();</span>
<span class="normal">            </span><span class="keyword">while</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">adj</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">].</span><span class="function">hasNext</span><span class="symbol">())</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">                stack</span><span class="symbol">.</span><span class="function">push</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">);</span>
<span class="normal">                v </span><span class="symbol">=</span><span class="normal"> adj</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">].</span><span class="function">next</span><span class="symbol">();</span>
<span class="normal">            </span><span class="cbracket">}</span>
<span class="normal">            </span><span class="comment">// add vertex with no more leaving edges to cycle</span>
<span class="normal">            cycle</span><span class="symbol">.</span><span class="function">push</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">);</span>
<span class="normal">        </span><span class="cbracket">}</span>

<span class="normal">        </span><span class="comment">// check if all edges have been used</span>
<span class="normal">        </span><span class="comment">// (in case there are two or more vertex-disjoint Eulerian cycles)</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">cycle</span><span class="symbol">.</span><span class="function">size</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">!=</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">E</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">+</span><span class="normal"> </span><span class="number">1</span><span class="symbol">)</span>
<span class="normal">            cycle </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">null</span><span class="symbol">;</span>

<span class="normal">        </span><span class="keyword">assert</span><span class="normal"> </span><span class="function">certifySolution</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Returns the sequence of vertices on an Eulerian cycle.</span>
<span class="comment">     * </span>
<span class="comment">     * </span><span class="type">@return</span><span class="comment"> the sequence of vertices on an Eulerian cycle;</span>
<span class="comment">     *         </span><span class="keyword">&lt;tt&gt;</span><span class="comment">null</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> if no such cycle</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="usertype">Iterable&lt;Integer&gt;</span><span class="normal"> </span><span class="function">cycle</span><span class="symbol">()</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="keyword">return</span><span class="normal"> cycle</span><span class="symbol">;</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Returns true if the digraph has an Eulerian cycle.</span>
<span class="comment">     * </span>
<span class="comment">     * </span><span class="type">@return</span><span class="comment"> </span><span class="keyword">&lt;tt&gt;</span><span class="comment">true</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> if the digraph has an Eulerian cycle;</span>
<span class="comment">     *         </span><span class="keyword">&lt;tt&gt;</span><span class="comment">false</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> otherwise</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="type">boolean</span><span class="normal"> </span><span class="function">hasEulerianCycle</span><span class="symbol">()</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="keyword">return</span><span class="normal"> cycle </span><span class="symbol">!=</span><span class="normal"> </span><span class="keyword">null</span><span class="symbol">;</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">// returns any non-isolated vertex; -1 if no such vertex</span>
<span class="normal">    </span><span class="keyword">private</span><span class="normal"> </span><span class="keyword">static</span><span class="normal"> </span><span class="type">int</span><span class="normal"> </span><span class="function">nonIsolatedVertex</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">outdegree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">)</span><span class="normal"> </span><span class="symbol">&gt;</span><span class="normal"> </span><span class="number">0</span><span class="symbol">)</span>
<span class="normal">                </span><span class="keyword">return</span><span class="normal"> v</span><span class="symbol">;</span>
<span class="normal">        </span><span class="keyword">return</span><span class="normal"> </span><span class="symbol">-</span><span class="number">1</span><span class="symbol">;</span>
<span class="normal">    </span><span class="cbracket">}</span>


<span class="normal">    </span><span class="comment">/**************************************************************************</span>
<span class="comment">     *</span>
<span class="comment">     *  The code below is solely for testing correctness of the data type.</span>
<span class="comment">     *</span>
<span class="comment">     **************************************************************************/</span>

<span class="normal">    </span><span class="comment">// Determines whether a digraph has an Eulerian cycle using necessary</span>
<span class="normal">    </span><span class="comment">// and sufficient conditions (without computing the cycle itself):</span>
<span class="normal">    </span><span class="comment">//    - at least one edge</span>
<span class="normal">    </span><span class="comment">//    - indegree(v) = outdegree(v) for every vertex</span>
<span class="normal">    </span><span class="comment">//    - the graph is connected, when viewed as an undirected graph</span>
<span class="normal">    </span><span class="comment">//      (ignoring isolated vertices)</span>
<span class="normal">    </span><span class="keyword">private</span><span class="normal"> </span><span class="keyword">static</span><span class="normal"> </span><span class="type">boolean</span><span class="normal"> </span><span class="function">hasEulerianCycle</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>

<span class="normal">        </span><span class="comment">// Condition 0: at least 1 edge</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">E</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">==</span><span class="normal"> </span><span class="number">0</span><span class="symbol">)</span><span class="normal"> </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// Condition 1: indegree(v) == outdegree(v) for every vertex</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">outdegree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">)</span><span class="normal"> </span><span class="symbol">!=</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">indegree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// Condition 2: graph is connected, ignoring isolated vertices</span>
<span class="normal">        </span><span class="usertype">Graph</span><span class="normal"> H </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Graph</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">());</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> w </span><span class="symbol">:</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">adj</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                H</span><span class="symbol">.</span><span class="function">addEdge</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">,</span><span class="normal"> w</span><span class="symbol">);</span>
<span class="normal">        </span>
<span class="normal">        </span><span class="comment">// check that all non-isolated vertices are conneted</span>
<span class="normal">        </span><span class="type">int</span><span class="normal"> s </span><span class="symbol">=</span><span class="normal"> </span><span class="function">nonIsolatedVertex</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>
<span class="normal">        </span><span class="usertype">BreadthFirstPaths</span><span class="normal"> bfs </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">BreadthFirstPaths</span><span class="symbol">(</span><span class="normal">H</span><span class="symbol">,</span><span class="normal"> s</span><span class="symbol">);</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">H</span><span class="symbol">.</span><span class="function">degree</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">)</span><span class="normal"> </span><span class="symbol">&gt;</span><span class="normal"> </span><span class="number">0</span><span class="normal"> </span><span class="symbol">&amp;&amp;</span><span class="normal"> </span><span class="symbol">!</span><span class="normal">bfs</span><span class="symbol">.</span><span class="function">hasPathTo</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">true</span><span class="symbol">;</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">// check that solution is correct</span>
<span class="normal">    </span><span class="keyword">private</span><span class="normal"> </span><span class="type">boolean</span><span class="normal"> </span><span class="function">certifySolution</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>

<span class="normal">        </span><span class="comment">// internal consistency check</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="function">hasEulerianCycle</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">==</span><span class="normal"> </span><span class="symbol">(</span><span class="function">cycle</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">==</span><span class="normal"> </span><span class="keyword">null</span><span class="symbol">))</span><span class="normal"> </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// hashEulerianCycle() returns correct value</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="function">hasEulerianCycle</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">!=</span><span class="normal"> </span><span class="function">hasEulerianCycle</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">))</span><span class="normal"> </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// nothing else to check if no Eulerian cycle</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">cycle </span><span class="symbol">==</span><span class="normal"> </span><span class="keyword">null</span><span class="symbol">)</span><span class="normal"> </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">true</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// check that cycle() uses correct number of edges</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">cycle</span><span class="symbol">.</span><span class="function">size</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">!=</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">E</span><span class="symbol">()</span><span class="normal"> </span><span class="symbol">+</span><span class="normal"> </span><span class="number">1</span><span class="symbol">)</span><span class="normal"> </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">false</span><span class="symbol">;</span>

<span class="normal">        </span><span class="comment">// check that cycle() is a directed cycle of G</span>
<span class="normal">        </span><span class="comment">// TODO</span>

<span class="normal">        </span><span class="keyword">return</span><span class="normal"> </span><span class="keyword">true</span><span class="symbol">;</span>
<span class="normal">    </span><span class="cbracket">}</span>


<span class="normal">    </span><span class="keyword">private</span><span class="normal"> </span><span class="keyword">static</span><span class="normal"> </span><span class="type">void</span><span class="normal"> </span><span class="function">unitTest</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">,</span><span class="normal"> </span><span class="usertype">String</span><span class="normal"> description</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">(</span><span class="normal">description</span><span class="symbol">);</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">(</span><span class="string">"-------------------------------------"</span><span class="symbol">);</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">print</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>

<span class="normal">        </span><span class="usertype">DirectedEulerianCycle</span><span class="normal"> euler </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">DirectedEulerianCycle</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>

<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">print</span><span class="symbol">(</span><span class="string">"Eulerian cycle: "</span><span class="symbol">);</span>
<span class="normal">        </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">euler</span><span class="symbol">.</span><span class="function">hasEulerianCycle</span><span class="symbol">())</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">            </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">:</span><span class="normal"> euler</span><span class="symbol">.</span><span class="function">cycle</span><span class="symbol">())</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">                StdOut</span><span class="symbol">.</span><span class="function">print</span><span class="symbol">(</span><span class="normal">v </span><span class="symbol">+</span><span class="normal"> </span><span class="string">" "</span><span class="symbol">);</span>
<span class="normal">            </span><span class="cbracket">}</span>
<span class="normal">            StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">();</span>
<span class="normal">        </span><span class="cbracket">}</span>
<span class="normal">        </span><span class="keyword">else</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">            StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">(</span><span class="string">"none"</span><span class="symbol">);</span>
<span class="normal">        </span><span class="cbracket">}</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">();</span>
<span class="normal">    </span><span class="cbracket">}</span>


<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Unit tests the </span><span class="keyword">&lt;tt&gt;</span><span class="comment">DirectedEulerianCycle</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> data type.</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="keyword">static</span><span class="normal"> </span><span class="type">void</span><span class="normal"> </span><span class="function">main</span><span class="symbol">(</span><span class="normal">String</span><span class="symbol">[]</span><span class="normal"> args</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="type">int</span><span class="normal"> V </span><span class="symbol">=</span><span class="normal"> Integer</span><span class="symbol">.</span><span class="function">parseInt</span><span class="symbol">(</span><span class="normal">args</span><span class="symbol">[</span><span class="number">0</span><span class="symbol">]);</span>
<span class="normal">        </span><span class="type">int</span><span class="normal"> E </span><span class="symbol">=</span><span class="normal"> Integer</span><span class="symbol">.</span><span class="function">parseInt</span><span class="symbol">(</span><span class="normal">args</span><span class="symbol">[</span><span class="number">1</span><span class="symbol">]);</span>

<span class="normal">        </span><span class="comment">// Eulerian cycle</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G1 </span><span class="symbol">=</span><span class="normal"> DigraphGenerator</span><span class="symbol">.</span><span class="function">eulerianCycle</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">,</span><span class="normal"> E</span><span class="symbol">);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G1</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"Eulerian cycle"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// Eulerian path</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G2 </span><span class="symbol">=</span><span class="normal"> DigraphGenerator</span><span class="symbol">.</span><span class="function">eulerianPath</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">,</span><span class="normal"> E</span><span class="symbol">);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G2</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"Eulerian path"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// empty digraph</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G3 </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Digraph</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G3</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"empty digraph"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// self loop</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G4 </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Digraph</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">);</span>
<span class="normal">        </span><span class="type">int</span><span class="normal"> v4 </span><span class="symbol">=</span><span class="normal"> StdRandom</span><span class="symbol">.</span><span class="function">uniform</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">);</span>
<span class="normal">        G4</span><span class="symbol">.</span><span class="function">addEdge</span><span class="symbol">(</span><span class="normal">v4</span><span class="symbol">,</span><span class="normal"> v4</span><span class="symbol">);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G4</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"single self loop"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// union of two disjoint cycles</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> H1 </span><span class="symbol">=</span><span class="normal"> DigraphGenerator</span><span class="symbol">.</span><span class="function">eulerianCycle</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">/</span><span class="number">2</span><span class="symbol">,</span><span class="normal"> E</span><span class="symbol">/</span><span class="number">2</span><span class="symbol">);</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> H2 </span><span class="symbol">=</span><span class="normal"> DigraphGenerator</span><span class="symbol">.</span><span class="function">eulerianCycle</span><span class="symbol">(</span><span class="normal">V </span><span class="symbol">-</span><span class="normal"> V</span><span class="symbol">/</span><span class="number">2</span><span class="symbol">,</span><span class="normal"> E </span><span class="symbol">-</span><span class="normal"> E</span><span class="symbol">/</span><span class="number">2</span><span class="symbol">);</span>
<span class="normal">        </span><span class="type">int</span><span class="symbol">[]</span><span class="normal"> perm </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="type">int</span><span class="symbol">[</span><span class="normal">V</span><span class="symbol">];</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> i </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> i </span><span class="symbol">&lt;</span><span class="normal"> V</span><span class="symbol">;</span><span class="normal"> i</span><span class="symbol">++)</span>
<span class="normal">            perm</span><span class="symbol">[</span><span class="normal">i</span><span class="symbol">]</span><span class="normal"> </span><span class="symbol">=</span><span class="normal"> i</span><span class="symbol">;</span>
<span class="normal">        StdRandom</span><span class="symbol">.</span><span class="function">shuffle</span><span class="symbol">(</span><span class="normal">perm</span><span class="symbol">);</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G5 </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Digraph</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">);</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> H1</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> w </span><span class="symbol">:</span><span class="normal"> H1</span><span class="symbol">.</span><span class="function">adj</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                G5</span><span class="symbol">.</span><span class="function">addEdge</span><span class="symbol">(</span><span class="normal">perm</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">],</span><span class="normal"> perm</span><span class="symbol">[</span><span class="normal">w</span><span class="symbol">]);</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> H2</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> w </span><span class="symbol">:</span><span class="normal"> H2</span><span class="symbol">.</span><span class="function">adj</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">))</span>
<span class="normal">                G5</span><span class="symbol">.</span><span class="function">addEdge</span><span class="symbol">(</span><span class="normal">perm</span><span class="symbol">[</span><span class="normal">V</span><span class="symbol">/</span><span class="number">2</span><span class="normal"> </span><span class="symbol">+</span><span class="normal"> v</span><span class="symbol">],</span><span class="normal"> perm</span><span class="symbol">[</span><span class="normal">V</span><span class="symbol">/</span><span class="number">2</span><span class="normal"> </span><span class="symbol">+</span><span class="normal"> w</span><span class="symbol">]);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G5</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"Union of two disjoint cycles"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// random digraph</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G6 </span><span class="symbol">=</span><span class="normal"> DigraphGenerator</span><span class="symbol">.</span><span class="function">simple</span><span class="symbol">(</span><span class="normal">V</span><span class="symbol">,</span><span class="normal"> E</span><span class="symbol">);</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G6</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"simple digraph"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// 4-vertex digraph</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G7 </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Digraph</span><span class="symbol">(</span><span class="keyword">new</span><span class="normal"> </span><span class="function">In</span><span class="symbol">(</span><span class="string">"eulerianD.txt"</span><span class="symbol">));</span>
<span class="normal">        </span><span class="function">unitTest</span><span class="symbol">(</span><span class="normal">G7</span><span class="symbol">,</span><span class="normal"> </span><span class="string">"4-vertex Eulerian digraph"</span><span class="symbol">);</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="cbracket">}</span>

<span class="comment">/******************************************************************************</span>
<span class="comment"> *  Copyright 2002-2015, Robert Sedgewick and Kevin Wayne.</span>
<span class="comment"> *</span>
<span class="comment"> *  This file is part of algs4.jar, which accompanies the textbook</span>
<span class="comment"> *</span>
<span class="comment"> *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,</span>
<span class="comment"> *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.</span>
<span class="comment"> *      </span><span class="url">http://algs4.cs.princeton.edu</span>
<span class="comment"> *</span>
<span class="comment"> *</span>
<span class="comment"> *  algs4.jar is free software: you can redistribute it and/or modify</span>
<span class="comment"> *  it under the terms of the GNU General Public License as published by</span>
<span class="comment"> *  the Free Software Foundation, either version 3 of the License, or</span>
<span class="comment"> *  (at your option) any later version.</span>
<span class="comment"> *</span>
<span class="comment"> *  algs4.jar is distributed in the hope that it will be useful,</span>
<span class="comment"> *  but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<span class="comment"> *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<span class="comment"> *  GNU General Public License for more details.</span>
<span class="comment"> *</span>
<span class="comment"> *  You should have received a copy of the GNU General Public License</span>
<span class="comment"> *  along with algs4.jar.  If not, see </span><span class="url">http://www.gnu.org/licenses.</span>
<span class="comment"> ******************************************************************************/</span>
</tt></pre>

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